离散时间Hopfield网络的动力系统分析

Analysis for Dynamics of Discrete Time Hopfield Network

离散时间的Hopfield网络模型是一个非线性动力系统 对网络的状态变量引入新的能量函数 ,利用凸函数次梯度性质可以得到网络状态能量单调减少的条件 对于神经元的连接权值且激活函数单调非减 (不一定严格单调增加 )的Hopfield网络 ,若神经元激活函数的增益大于权值矩阵的最小特征值 ,则全并行时渐进收敛 ;而当网络串行时 ,只要网络中每个神经元激活函数的增益与该神经元的自反馈连接权值的和大于零即可 同时 ,若神经元激活函数单调 ,网络连接权值对称 ,利用凸函数次梯度的性质 ,证明了离散时间的Hopfield网络模型全并行时收敛到周期不大于

Hopfield network model with discrete time is a nonlinear dynamic system With introduced new energy functions for the state variables of network in this paper, the condition under which the state energy of network will decrease monotonously can be derived by the subgradient property of convex function For Hopfield network with the symmetrical synapse connections among neurons and the no decreasing (not necessary to increase strictly) activation function of each neuron, it will be convergent asymptotically in parallel mode if the gain of neuron activation function is greater than eigenvalue of minimization, and so is it in asynchronous mode if the sum of the gain of neuron activation function and the synapse weight of neuron self feedback connection is greater than zero By using of subgradient property of convex function, it will converge to a limit cycle with period less than 2 in parallel mode for discrete time Hopfield network model with the symmetrical synapse connections among neurons and the no decreasing (not necessary to increase strictly) activation function of each neuron